Discretization of the Density Matrix as a Nonlinear Positive Map and Entanglement

Abstract

We propose the discretization of the density matrix as a nonlinear positive map for systems with continuous variables. We use this procedure for calculating the entanglement between two modes through different criteria, such as Tsallis entropy, von Neumann entropy and linear entropy, and the logarithmic negativity. As an example, we study the dynamics of entanglement for the two-mode squeezed-vacuum state in the parametric amplifier and show good agreement with the analytic results. Also we address the loss of information on the system state due to the discretization of the density matrix.